Among the known hydrides, Fmm-LaH\(_{10}\)  possesses superior superconducting behaviors with the maximum \(T_c\)  above 250 K. Considerable efforts are devoted to maintain the high symmetry phase of LaH\(_{10}\)  at lower pressures to preserve high \(T_c\)  values. However, owing to the strong instability, a structural distortion from Fmm to C/2m phase of LaH\(_{10}\)  leads to a steep drop of \(T_c\)  with decreasing pressure [1]}. Introducing extra electrons via metal doping into the hydrogen-rich materials is supposed to effectively reduce the metallization pressure [2]}, [3]}, [4]}. The delocalized Ce 4f electrons contribute to chemical pre-compression in cerium hydrides at pressure below 1 megabar with \(T_c\)  as high as 115 K [5]}, [6]}. Hence, one can expect low-pressure stability of high-\(T_c\)  superconducting Fmm phase of LaH\(_{10}\)  by introducing the Ce 4f electrons. A recent experimental work demonstrates the synthesis of P6\(_3\) /mmc La\(_{0.5}\) Ce\(_{0.5}\) H\(_{9}\)  with \(T_c\)  up to 178 K [7]}. Concurrently, superconductivity with \(T_c\)  up to 190 K was reported in ternary polyhydrides hcp-(La,Ce)H\(_{9-10}\)  and fcc-(La,Ce)H\(_{9-10}\)[8]}. The uncertainties of the atomic ratio between La and Ce make difficult in performing the theoretical calculations in order to compare the results with experiments and thus hard to understand the behind microscopic mechanism of superconductivity in these La-Ce superhydrides.
